A bloc of Senate Democrats have said they won't support a floor vote until late May.
"She said ... I’ll do it, period,” Rep. Elijah Cummings (Md.) said.
Hagel said the unrest would be "factored in" to decisions on releasing detainees.
Obama will deliver his penultimate State of the Union address.
A top U.S. commander in Iraq said the terror groups is switching to "defense."
The bill will level new sanctions on Russia and pave the way for lethal arms to Ukraine.
John Brennan delivered an aggressive rebuttal of the Senate Intelligence panel's report.
The 528-page report asserts that the CIA tortured and misled the public.
The bill passed on a bipartisan vote of 300-119, and now heads to the Senate.
Negotiators unveiled the proposed cuts as part of a 2015 defense authorization bill.
The Pentagon reversed its decision to wait until Congress approved funding.
Republican leaders picked new chairmen for Armed Services and Intelligence.
The hearing came days before the administration releases its 2016 Defense budget request.
Senators introduced a bill in support of allowing talks to conclude before sanctions legislation.
The administration is objecting to an up-or-down vote in Congress on a deal.
Tuesday's SOTU wil be the first since the U.S. stepped up the fight against ISIS.
Fifteen aircraft conducted 45 strikes in northwestern Iraq earlier this month.
Sens.-elect Tom Cotton (Ark.) and Joni Ernst (Iowa) are joining the panel.
"We will have hearings in January, February, March," said Rep. Trey Gowdy.
The Joint Chiefs urged commanders to "take appropriate force protection measures."
"This war is illegal until Congress acts," said Paul.
Coalition forces launched 55 airstrikes against multiple targets in Iraq and Syria.
Reports say the Pentagon could face a $60 billion shortfall.
The secretary of State said U.S. strategy against ISIS is "starting to gain traction."